1358:
622:
509:, another key ferroelectric material, although the structure is rather similar to barium titanate the driving force for ferroelectricity is more complex with interactions between the lead and oxygen ions also playing an important role. In an order-disorder ferroelectric, there is a dipole moment in each unit cell, but at high temperatures they are pointing in random directions. Upon lowering the temperature and going through the phase transition, the dipoles order, all pointing in the same direction within a domain.
307:. Sabatier principle states that the surface-adsorbates interaction has to be an optimal amount: not too weak to be inert toward the reactants and not too strong to poison the surface and avoid desorption of the products: a compromise situation. This set of optimum interactions is usually referred to as "top of the volcano" in activity volcano plots. On the other hand, ferroelectric polarization-dependent chemistry can offer the possibility of switching the surfaceâadsorbates interaction from strong
1353:{\displaystyle {\begin{array}{ll}\Delta E=&{\frac {1}{2}}\alpha _{0}\left(T-T_{0}\right)\left(P_{x}^{2}+P_{y}^{2}+P_{z}^{2}\right)+{\frac {1}{4}}\alpha _{11}\left(P_{x}^{4}+P_{y}^{4}+P_{z}^{4}\right)\\&+{\frac {1}{2}}\alpha _{12}\left(P_{x}^{2}P_{y}^{2}+P_{y}^{2}P_{z}^{2}+P_{z}^{2}P_{x}^{2}\right)\\&+{\frac {1}{6}}\alpha _{111}\left(P_{x}^{6}+P_{y}^{6}+P_{z}^{6}\right)\\&+{\frac {1}{2}}\alpha _{112}\left\\&+{\frac {1}{2}}\alpha _{123}P_{x}^{2}P_{y}^{2}P_{z}^{2}\end{array}}}
156:
148:
140:
551:, and the prediction could immediately be verified by several observations of behavior connected to ferroelectricity in smectic liquid-crystal phases that are chiral and tilted. The technology allows the building of flat-screen monitors. Mass production between 1994 and 1999 was carried out by Canon. Ferroelectric liquid crystals are used in production of reflective
350:
surface charge. This can cause current flow in the case of a ferroelectric capacitor even without the presence of an external voltage across the capacitor. Two stimuli that will change the lattice dimensions of a material are force and temperature. The generation of a surface charge in response to the application of an external stress to a material is called
36:
285:) in which a contact is made up by nanometer-thick ferroelectric film placed between metal electrodes. The thickness of the ferroelectric layer is small enough to allow tunneling of electrons. The piezoelectric and interface effects as well as the depolarization field may lead to a giant electroresistance (GER) switching effect.
3001:
520:
lead zirconate. Different compositions are used for different applications; for memory applications, PZT closer in composition to lead titanate is preferred, whereas piezoelectric applications make use of the diverging piezoelectric coefficients associated with the morphotropic phase boundary that is
349:
The internal electric dipoles of a ferroelectric material are coupled to the material lattice so anything that changes the lattice will change the strength of the dipoles (in other words, a change in the spontaneous polarization). The change in the spontaneous polarization results in a change in the
271:
make ferroelectric capacitors very useful, e.g. for sensor applications. Ferroelectric capacitors are used in medical ultrasound machines (the capacitors generate and then listen for the ultrasound ping used to image the internal organs of a body), high quality infrared cameras (the infrared image is
243:
simply consists of a pair of electrodes sandwiching a layer of ferroelectric material. The permittivity of ferroelectrics is not only adjustable but commonly also very high, especially when close to the phase transition temperature. Because of this, ferroelectric capacitors are small in physical size
259:
cards. In these applications thin films of ferroelectric materials are typically used, as this allows the field required to switch the polarization to be achieved with a moderate voltage. However, when using thin films a great deal of attention needs to be paid to the interfaces, electrodes and
1791:
3193:
2016:
4612:
Wanlin Zhu, John Hayden, Fan He, Jung-In Yang, Pannawit
Tipsawat, Mohammad D. Hossain, Jon-Paul Maria, and Susan Trolier-McKinstry, "Strongly temperature dependent ferroelectric switching in AlN, Al1-xScxN, and Al1-xBxN thin films", Appl. Phys. Lett. 119, 062901 (2021)
302:
of these materials. Surface-perpendicular component of the ferroelectric polarization can dope polarization-dependent charges on surfaces of ferroelectric materials, changing their chemistry. This opens the possibility of performing catalysis beyond the limits of the
4662:
4749:
Cao, Yanwei; Wang, Zhen; Park, Se Young; Yuan, Yakun; Liu, Xiaoran; Nikitin, Sergey M.; Akamatsu, Hirofumi; Kareev, M.; Middey, S.; Meyers, D.; Thompson, P.; Ryan, P. J.; Shafer, Padraic; NâDiaye, A.; Arenholz, E.; Gopalan, Venkatraman; Zhu, Yimei;
3328:
4460:
Benke, Annegret; Mehner, Erik; Rosenkranz, Marco; Dmitrieva, Evgenia; Leisegang, Tilmann; StĂścker, Hartmut; Pompe, Wolfgang; Meyer, Dirk C. (30 July 2015). "Pyroelectrically Driven â˘OH Generation by Barium
Titanate and Palladium Nanoparticles".
505:. This leads to an asymmetrical shift in the equilibrium ion positions and hence to a permanent dipole moment. The ionic displacement in barium titanate concerns the relative position of the titanium ion within the oxygen octahedral cage. In
272:
projected onto a two dimensional array of ferroelectric capacitors capable of detecting temperature differences as small as millionths of a degree
Celsius), fire sensors, sonar, vibration sensors, and even fuel injectors on diesel engines.
2327:
2820:
2782:
3424:). Elimination of this region, and connection of the top and bottom portions of the 'S' curve by vertical lines at the discontinuities gives the hysteresis loop of internal polarization due to an external electric field.
1633:
3027:
224:) and are paraelectric above this temperature: the spontaneous polarization vanishes, and the ferroelectric crystal transforms into the paraelectric state. Many ferroelectrics lose their pyroelectric properties above
3422:
2187:
2651:
1869:
497:, a typical ferroelectric of the displacive type, the transition can be understood in terms of a polarization catastrophe, in which, if an ion is displaced from equilibrium slightly, the force from the local
2488:
1456:
198:
by a suitably strong applied electric field in the opposite direction; the polarization is therefore dependent not only on the current electric field but also on its history, yielding a
3432:
Sliding ferroelectricity is widely found but only in two-dimensional (2D) van der Waals stacked layers. The vertical electric polarization is switched by in-plane interlayer sliding.
592:
It should be possible to produce materials which combine both ferroelectric and metallic properties simultaneously, at room temperature. According to research published in 2018 in
1545:
1611:
1578:
1512:
3201:
2687:
292:, where researchers are looking for ways to couple magnetic and ferroelectric ordering within a material or heterostructure; there are several recent reviews on this topic.
1462:. Typically, this involves adding a gradient term, an electrostatic term and an elastic term to the free energy. The equations are then discretized onto a grid using the
298:
properties of ferroelectrics have been studied since 1952 when
Parravano observed anomalies in CO oxidation rates over ferroelectric sodium and potassium niobates near the
1834:
1458:
must be consistent with the crystal symmetry. To investigate domain formation and other phenomena in ferroelectrics, these equations are often used in the context of a
54:
5075:
2217:
1861:
596:, scientists were able to produce a two-dimensional sheet of material which was both ferroelectric (had a polar crystal structure) and which conducted electricity.
2996:{\displaystyle \Delta E={\frac {1}{2}}\alpha _{0}\left(T-T_{0}\right)P_{x}^{2}+{\frac {1}{4}}\alpha _{11}P_{x}^{4}+{\frac {1}{6}}\alpha _{111}P_{x}^{6}-E_{x}P_{x}}
4171:
Kolpak, Alexie M.; Grinberg, Ilya; Rappe, Andrew M. (2007-04-16). "Polarization
Effects on the Surface Chemistry of $ {\mathrm{PbTiO}}_{3}$ -Supported Pt Films".
5009:
570:" properties, and may have wide-ranging applications in device and nano-technology and also influence the electrical nature of dust in the interstellar medium.
123:, meaning iron, was used to describe the property despite the fact that most ferroelectric materials do not contain iron. Materials that are both ferroelectric
4285:
Laursen, Anders B.; Man, Isabela
Costinela; Trinhammer, Ole L.; Rossmeisl, Jan; Dahl, Søren (December 2011). "The Sabatier Principle Illustrated by Catalytic H
2695:
331:
effects under varying temperature (heating/cooling cycles) or varying strain (vibrations) conditions extra charges can appear on the surface and drive various
1786:{\displaystyle \Delta E={\frac {1}{2}}\alpha _{0}\left(T-T_{0}\right)P_{x}^{2}+{\frac {1}{4}}\alpha _{11}P_{x}^{4}+{\frac {1}{6}}\alpha _{111}P_{x}^{6}}
3188:{\displaystyle {\frac {\partial \Delta E}{\partial P_{x}}}=\alpha _{0}\left(T-T_{0}\right)P_{x}+\alpha _{11}P_{x}^{3}+\alpha _{111}P_{x}^{5}-E_{x}=0}
183:, corresponding to the slope of the polarization curve, is not constant as in linear dielectrics but is a function of the external electric field.
3362:
2024:
263:
Ferroelectric materials are required by symmetry considerations to be also piezoelectric and pyroelectric. The combined properties of memory,
4962:
4943:
4921:
4592:
3805:
3650:
3625:
2011:{\displaystyle {\frac {\partial \Delta E}{\partial P_{x}}}=\alpha _{0}\left(T-T_{0}\right)P_{x}+\alpha _{11}P_{x}^{3}+\alpha _{111}P_{x}^{5}}
1547:. These coefficients may be obtained experimentally or from ab-initio simulations. For ferroelectrics with a first order phase transition,
1627:
of a ferroelectric for a cubic to tetragonal phase transition may be obtained by considering the 1D expression of the free energy which is:
4709:
2499:
2493:
and eliminating solutions which take the square root of a negative number (for either the first or second order phase transitions) gives:
341:
is a technique to record optical information on pieces of ferroelectric material. The images are nonvolatile and selectively erasable.
3780:
5002:
4436:
72:
175:; so the polarization is a linear function. This is called linear dielectric polarization (see figure). Some materials, known as
5080:
4713:
3878:
M.Ye. Zhuravlev; R.F. Sabirianov; S.S. Jaswal; E.Y. Tsymbal (2005). "Giant
Electroresistance in Ferroelectric Tunnel Junctions".
3446:
2338:
4328:
Seh, Zhi Wei; Kibsgaard, Jakob; Dickens, Colin F.; Chorkendorff, Ib; Nørskov, Jens K.; Jaramillo, Thomas F. (13 January 2017).
4488:
Kakekhani, Arvin; Ismail-Beigi, Sohrab (2016). "Ferroelectric oxide surface chemistry: water splitting via pyroelectricity".
3472:
1836:, the spontaneous polarization. We find the derivative of the free energy, and set it equal to zero in order to solve for
1399:
373:. Among the piezoelectric classes, 10 have a spontaneous electric polarization which varies with temperature; thus they are
4735:
5085:
3585:
608:, the free energy of a ferroelectric material, in the absence of an electric field and applied stress may be written as a
277:
315:, thus a compromise between desorption and adsorption is no longer needed. Ferroelectric polarization can also act as an
239:
The nonlinear nature of ferroelectric materials can be used to make capacitors with adjustable capacitance. Typically, a
4995:
4329:
559:
384:
103:, with the additional property that their natural electrical polarization is reversible. The term is used in analogy to
4626:
Clark, Noel A.; Lagerwall, Sven T. (June 1980). "Submicrosecond bistable electroâoptic switching in liquid crystals".
605:
377:. Ferroelectricity is a subset of pyroelectricity, which brings spontaneous electronic polarization to the material.
4680:
3613:
3478:
477:
338:
5090:
4206:
Yun, Yang; Altman, Eric I. (December 2007). "Using
Ferroelectric Poling to Change Adsorption on Oxide Surfaces".
616:. If a sixth order expansion is used (i.e. 8th order and higher terms truncated), the free energy is given by:
213:
Typically, materials demonstrate ferroelectricity only below a certain phase transition temperature, called the
3534:
1463:
186:
In addition to being nonlinear, ferroelectric materials demonstrate a spontaneous nonzero polarization (after
4982:
3451:
578:
513:
435:
240:
3356:
529:
354:. A change in the spontaneous polarization of a material in response to a change in temperature is called
3466:
1517:
1467:
187:
3323:{\displaystyle E_{x}=\alpha _{0}\left(T-T_{0}\right)P_{e}+\alpha _{11}P_{e}^{3}+\alpha _{111}P_{e}^{5}}
1583:
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1484:
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3514:
164:
92:
2659:
251:
effect which can be used as a memory function, and ferroelectric capacitors are indeed used to make
320:
95:
that can be reversed by the application of an external electric field. All ferroelectrics are also
89:
4844:"Sliding ferroelectricity in 2D van der Waals materials: Related physics and future opportunities"
4681:"Pyroelectric Materials for Uncooled Infrared Detectors: Processing, Properties, and Applications"
566:
or propane exhibited ferroelectric properties. This new class of ferroelectric materials exhibit "
194:
is zero. The distinguishing feature of ferroelectrics is that the spontaneous polarization can be
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4042:
4003:
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574:
517:
304:
4679:
Aggarwal, M.D.; A.K. Batra; P. Guggilla; M.E. Edwards; B.G. Penn; J.R. Currie Jr. (March 2010).
155:
147:
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4939:
4917:
4883:
4803:
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4538:
4432:
4401:
4352:
4223:
4188:
4034:
3995:
3960:
3801:
3776:
3646:
3621:
3460:
2322:{\displaystyle \alpha _{0}\left(T-T_{0}\right)+\alpha _{11}P_{s}^{2}+\alpha _{111}P_{s}^{4}=0}
1475:
582:
456:
332:
316:
299:
252:
214:
3970:
W. Eerenstein; N.D. Mathur; J.F. Scott (2006). "Multiferroic and magnetoelectric materials".
17:
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4873:
4863:
4793:
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541:
403:
370:
351:
328:
264:
96:
3496: â Electrically insulating substance able to be polarised by an applied electric field
1839:
485:
Ferroelectric phase transitions are often characterized as either displacive (such as BaTiO
5034:
3519:
3508:
3493:
548:
516:(PZT), which is part of the solid solution formed between ferroelectric lead titanate and
502:
494:
442:
416:
374:
355:
324:
268:
176:
108:
100:
2777:{\displaystyle P_{s}=\pm {\sqrt{\frac {\alpha _{0}\left(T_{0}-T\right)}{\alpha _{111}}}}}
1796:
This free energy has the shape of a double well potential with two free energy minima at
4859:
4781:
4639:
4306:
4261:
4147:
4108:
4065:
3983:
3948:
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3848:
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369:
can be found in crystals. There are 21 non-centrosymmetric classes, within which 20 are
139:
4878:
4843:
4798:
4755:
4095:
Parravano, G. (February 1952). "Ferroelectric
Transitions and Heterogenous Catalysis".
4014:
3932:
1471:
567:
537:
498:
395:
366:
116:
104:
4378:
Zhang, Yan; Xie, Mengying; Adamaki, Vana; Khanbareh, Hamideh; Bowen, Chris R. (2017).
231:
completely, because their paraelectric phase has a centrosymmetric crystal structure.
5069:
4955:
Effective Field
Approach to Phase Transitions and Some Applications to Ferroelectrics
4931:
4895:
4751:
4446:
4380:"Control of electro-chemical processes using energy harvesting materials and devices"
4364:
4330:"Combining theory and experiment in electrocatalysis: Insights into materials design"
4081:
4073:
4046:
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609:
563:
506:
449:
289:
207:
203:
128:
112:
3917:
3555: â materials that exhibit more than one of the primary ferroic order parameters
4663:"Novel ferroelectric behaviour of N2O films: spontaneous potentials of up to 40 V."
4007:
3864:
180:
111:. Ferromagnetism was already known when ferroelectricity was discovered in 1920 in
4184:
3909:
493:), though often phase transitions will demonstrate elements of both behaviors. In
179:
materials, show a more enhanced nonlinear polarization (see figure). The electric
4584:
4517:"Piezopotential-Driven Redox Reactions at the Surface of Piezoelectric Materials"
5018:
4419:
Fang, Liang; You, Lu; Liu, Jun-Ming (2018). "Ferroelectrics in Photocatalysis".
3540:
362:
4789:
4572:
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533:
466:
462:
312:
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248:
199:
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4348:
4030:
3505: â Electric charge generated in certain solids due to mechanical stress
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4807:
4542:
4533:
4516:
4405:
4356:
4227:
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3964:
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501:
due to the ions in the crystal increases faster than the elastic-restoring
4821:
P. Chandra; P.B. Littlewood (2006). "A Landau Primer for Ferroelectrics".
4827:
4132:"Ferroelectrics: A pathway to switchable surface chemistry and catalysis"
4017:; Fiebig, M. (2005). "The renaissance of magnetoelectric multiferroics".
3892:
3839:
525:
3991:
3733:
3417:{\displaystyle {\frac {\partial ^{2}\Delta E}{\partial P_{x}^{2}}}<0}
2182:{\displaystyle 0={\frac {\partial \Delta E}{\partial P_{x}}}=P_{s}\left}
585:. A single atom thick ferroelectric monolayer can be created using pure
244:
compared to dielectric (non-tunable) capacitors of similar capacitance.
171:, is almost exactly proportional to the applied external electric field
4501:
4396:
4379:
4130:
Kakekhani, Arvin; Ismail-Beigi, Sohrab; Altman, Eric I. (August 2016).
3549: â An inorganic, nonmetallic solid prepared by the action of heats
3546:
3522: â phenomenon in which a material may exhibit a spontaneous strain
3469: â Group of crystalline polar polymers that are also ferroelectric
3347:(but on the Y axis) gives an S-shaped curve which is multi-valued in P
2795:) may be obtained from the free energy expansion by including the term
586:
4987:
4314:
4219:
4116:
3956:
473:
4647:
4614:
3700:
3668:
3616:. In Frederick Seitz; T. P. Das; David Turnbull; E. L. Hahn (eds.).
2646:{\displaystyle P_{s}=\pm {\sqrt {{\frac {1}{2\alpha _{111}}}\left}}}
547:
In 1974 R.B. Meyer used symmetry arguments to predict ferroelectric
4772:
3643:
Principles and applications of ferroelectrics and related materials
3825:; J.F. Scott (2005). "Physics of thin-film ferroelectric oxides".
247:
The spontaneous polarization of ferroelectric materials implies a
138:
4573:"Piezoelectric and Pyroelectric Materials and Their Applications"
3017:, again by setting the derivative of the energy with respect to P
4736:"Rutgers Physicists Create New Class of 2D Artificial Materials"
4687:
3765:
Piezoelectric and acoustic materials for transducer applications
552:
256:
4991:
3935:(2007). "Multiferroics: Progress and prospects in thin films".
2806:
corresponding to the energy due to an external electric field E
2200:
solution of this equation rather corresponds to a free energy
29:
4571:
Whatmore, R. W. (1991), Miller, L. S.; Mullin, J. B. (eds.),
4246:"Ferroelectric-Based Catalysis: Switchable Surface Chemistry"
604:
An introduction to Landau theory can be found here. Based on
544:
in some ferroelectric crystals is still not well understood.
4756:"Artificial two-dimensional polar metal at room temperature"
3440:
3355:. The central part of the 'S' corresponds to a free energy
2689:, the solution for the spontaneous polarization reduces to:
4515:
Starr, Matthew B.; Shi, Jian; Wang, Xudong (11 June 2012).
4052:
M. Fiebig (2005). "Revival of the magnetoelectric effect".
4710:"Discovery of ferroelectricity in an elementary substance"
4558:
McGraw-Hill Concise Encyclopedia of Science and Technology
2483:{\displaystyle P_{s}^{2}={\frac {1}{2\alpha _{111}}}\left}
319:. Polarization can help the separation of photo-generated
4666:
Poster Session Presented at ECAMP 2010, Salamanca, Spain.
4914:
Domain Structure in Ferroelectrics and Related Materials
3475: â Microscopy technique for piezoelectric materials
512:
An important ferroelectric material for applications is
4244:
Kakekhani, Arvin; Ismail-Beigi, Sohrab (29 June 2015).
3575:
Pages displaying short descriptions of redirect targets
3498:
Pages displaying short descriptions of redirect targets
3481: â Imaging technique using ferroelectric materials
50:
3701:"Piezo-Electric and Allied Phenomena in Rochelle Salt"
3543: â Solid-state electronics based on electron spin
2204:
in the ferroelectric phase, the desired solutions for
1451:{\displaystyle \alpha _{i},\alpha _{ij},\alpha _{ijk}}
379:
3767:. Springer Science & Business Media. p. 21.
3669:"Piezoelectric and allied phenomena in Rochelle salt"
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are the components of the polarization vector in the
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is a characteristic of certain materials that have a
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Pages displaying wikidata descriptions as a fallback
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Pages displaying wikidata descriptions as a fallback
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Pages displaying wikidata descriptions as a fallback
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correspond to setting the remaining factor to zero:
414:
401:
202:
loop. They are called ferroelectrics by analogy to
3454: â capacitor based on a ferroelectric material
323:, leading to enhanced photocatalysis. Also, due to
45:
may be too technical for most readers to understand
4556:Land, Cecil (2004). "Photoferroelectric imaging".
3573: â Phenomena involving electrical occurrences
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3582: â Overview of and topical guide to physics
3511: â Voltage created when a crystal is heated
4936:Physics of Ferroelectrics: A modern perspective
4848:Proceedings of the National Academy of Sciences
4421:Ferroelectric Materials for Energy Applications
1396:directions respectively, and the coefficients,
27:Characteristic of certain crystalline materials
4577:Electronic Materials: From Silicon to Organics
562:found that prosaic films of chemicals such as
5003:
4579:, Boston, MA: Springer US, pp. 283â290,
3531: â Polarization due to a strain gradient
260:sample quality for devices to work reliably.
8:
4934:; Jean-Marc Triscone; Charles H Ahn (2007).
3006:We find the stable polarization values of P
573:Other ferroelectric materials used include
107:, in which a material exhibits a permanent
5010:
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3620:. Vol. 4. Academic Press. p. 5.
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190:, see figure) even when the applied field
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1097:
1092:
1077:
1063:
1044:
1039:
1026:
1021:
1008:
1003:
988:
974:
955:
950:
940:
935:
922:
917:
907:
902:
889:
884:
874:
869:
854:
840:
821:
816:
803:
798:
785:
780:
765:
751:
737:
732:
719:
714:
701:
696:
676:
655:
641:
626:
624:
73:Learn how and when to remove this message
57:, without removing the technical details.
4842:Wu, Menghao; Li, Ju (14 December 2021).
4208:Journal of the American Chemical Society
425:
420:
409:
407:
154:
146:
4521:Angewandte Chemie International Edition
3614:"Ferroelectrics and Antiferroelectrics"
3604:
275:Another idea of recent interest is the
5076:Electric and magnetic fields in matter
3747:Chiang, Y. et al.: Physical Ceramics,
521:found close to the 50/50 composition.
288:Yet another burgeoning application is
210:and exhibit similar hysteresis loops.
4239:
4237:
4054:Journal of Physics D: Applied Physics
3463: â Novel type of computer memory
1613:for a second order phase transition.
55:make it understandable to non-experts
7:
4560:(5 ed.). New York: McGraw-Hill.
4463:The Journal of Physical Chemistry C
2810:interacting with the polarization P
4754:; Chakhalian, J. (18 April 2018).
4293:Decomposition on Metal Surfaces".
3387:
3379:
3370:
3045:
3037:
3034:
2824:
2048:
2040:
2037:
1887:
1879:
1876:
1637:
1540:{\displaystyle \alpha _{111}>0}
630:
206:materials, which have spontaneous
25:
4615:https://doi.org/10.1063/5.0057869
3340:(on the X axis) as a function of
1606:{\displaystyle \alpha _{11}>0}
1573:{\displaystyle \alpha _{11}<0}
612:in terms of the order parameter,
489:) or order-disorder (such as NaNO
4714:National University of Singapore
4490:Journal of Materials Chemistry A
3447:Category:Ferroelectric materials
1507:{\displaystyle \alpha _{0}>0}
34:
4097:The Journal of Chemical Physics
4916:. Cambridge University Press.
4668:– via Aarhus University.
3473:Piezoresponse force microscopy
2682:{\displaystyle \alpha _{11}=0}
143:Linear dielectric polarization
1:
4295:Journal of Chemical Education
4185:10.1103/PhysRevLett.98.166101
3910:10.1103/PhysRevLett.94.246802
3586:Index of electronics articles
1481:In all known ferroelectrics,
278:ferroelectric tunnel junction
18:Ferro-electric liquid crystal
4585:10.1007/978-1-4615-3818-9_19
540:crystals. The nature of the
428:
167:, the polarization induced,
3645:. Clarendon Press, Oxford.
3641:M. Lines; A. Glass (1979).
1829:{\displaystyle P_{x}=P_{s}}
534:domain structure hysteresis
333:(electro)chemical reactions
127:ferromagnetic are known as
5107:
4790:10.1038/s41467-018-03964-9
4157:10.1016/j.susc.2015.10.055
4074:10.1088/0022-3727/38/8/R01
3857:10.1103/RevModPhys.77.1083
3479:Photoferroelectric imaging
339:Photoferroelectric imaging
159:Ferroelectric polarization
5025:
4953:Julio A. Gonzalo (2006).
4429:10.1002/9783527807505.ch9
3827:Reviews of Modern Physics
3537: â Branch of physics
390:
382:
361:Generally, there are 230
151:Paraelectric polarization
4475:10.1021/acs.jpcc.5b04589
4384:Chemical Society Reviews
4271:10.1021/acscatal.5b00507
3535:Condensed matter physics
3428:Sliding ferroelectricity
1618:spontaneous polarization
1464:finite difference method
163:When most materials are
5081:Ferroelectric materials
4983:University of Cambridge
4979:Ferroelectric Materials
4912:A. S. Sidorkin (2006).
4869:10.1073/pnas.2115703118
4661:Plekan, Oksana (2010).
4628:Applied Physics Letters
4349:10.1126/science.aad4998
4173:Physical Review Letters
4031:10.1126/science.1113357
3880:Physical Review Letters
3452:Ferroelectric capacitor
579:polyvinylidene fluoride
530:transition temperatures
514:lead zirconate titanate
241:ferroelectric capacitor
4534:10.1002/anie.201201424
3798:Ferroelectric Memories
3763:Safari, Ahmad (2008).
3725:10.1103/PhysRev.17.475
3693:10.1103/PhysRev.15.505
3612:Werner Känzig (1957).
3418:
3324:
3189:
2997:
2787:The hysteresis loop (P
2778:
2683:
2647:
2484:
2323:
2183:
2012:
1857:
1830:
1787:
1607:
1574:
1541:
1508:
1452:
1354:
606:GinzburgâLandau theory
391:21 noncentrosymmetric
165:electrically polarized
160:
152:
144:
4760:Nature Communications
3750:John Wiley & Sons
3467:Ferroelectric polymer
3419:
3325:
3190:
2998:
2779:
2684:
2648:
2485:
2324:
2184:
2013:
1858:
1856:{\displaystyle P_{s}}
1831:
1788:
1608:
1575:
1542:
1509:
1468:finite element method
1453:
1355:
594:Nature Communications
158:
150:
142:
93:electric polarization
5086:Electrical phenomena
5045:antiferroelectricity
4957:. World Scientific.
4423:. pp. 265â309.
3571:Electrical phenomena
3515:Antiferroelectricity
3363:
3351:for some values of E
3202:
3028:
2821:
2696:
2660:
2500:
2339:
2218:
2025:
1870:
1840:
1800:
1634:
1584:
1551:
1518:
1485:
1400:
623:
5019:Polarization states
4860:2021PNAS..11815703W
4854:(50): e2115703118.
4782:2018NatCo...9.1547C
4640:1980ApPhL..36..899C
4469:(32): 18278â18286.
4307:2011JChEd..88.1711L
4262:2015APS..MARY26011K
4214:(50): 15684â15689.
4148:2016SurSc.650..302K
4109:1952JChPh..20..342P
4066:2005JPhD...38R.123F
3992:10.1038/nature05023
3984:2006Natur.442..759E
3949:2007NatMa...6...21R
3902:2005PhRvL..94x6802Z
3849:2005RvMP...77.1083D
3796:J.F. Scott (2000).
3773:2008pamt.book.....S
3717:1921PhRv...17..475V
3699:J. Valasek (1921).
3685:1920PhRv...15..505.
3667:J. Valasek (1920).
3618:Solid State Physics
3404:
3319:
3291:
3165:
3137:
2969:
2931:
2893:
2580:
2419:
2356:
2332:whose solution is:
2312:
2284:
2173:
2145:
2007:
1979:
1782:
1744:
1706:
1345:
1330:
1315:
1262:
1244:
1224:
1201:
1183:
1163:
1140:
1122:
1102:
1049:
1031:
1013:
960:
945:
927:
912:
894:
879:
826:
808:
790:
742:
724:
706:
528:often show several
385:Crystalline classes
367:crystalline classes
321:electron-hole pairs
119:. Thus, the prefix
4502:10.1039/C6TA00513F
4397:10.1039/c7cs00387k
4343:(6321): eaad4998.
3580:Outline of physics
3414:
3390:
3320:
3305:
3277:
3185:
3151:
3123:
3013:, now denoted as P
2993:
2955:
2917:
2879:
2774:
2679:
2643:
2566:
2480:
2405:
2342:
2319:
2298:
2270:
2179:
2159:
2131:
2008:
1993:
1965:
1853:
1826:
1783:
1768:
1730:
1692:
1603:
1570:
1537:
1504:
1448:
1350:
1348:
1331:
1316:
1301:
1248:
1230:
1210:
1187:
1169:
1149:
1126:
1108:
1088:
1035:
1017:
999:
946:
931:
913:
898:
880:
865:
812:
794:
776:
728:
710:
692:
575:triglycine sulfate
518:anti-ferroelectric
429:non ferroelectric
410:non piezoelectric
305:Sabatier principle
255:for computers and
161:
153:
145:
5063:
5062:
4964:978-981-256-875-5
4945:978-3-540-34591-6
4923:978-1-904602-14-9
4594:978-1-4615-3818-9
4527:(24): 5962â5966.
4496:(14): 5235â5246.
4390:(24): 7757â7786.
4315:10.1021/ed101010x
4301:(12): 1711â1715.
4220:10.1021/ja0762644
4117:10.1063/1.1700412
3807:978-3-540-66387-4
3652:978-0-19-851286-8
3627:978-0-12-607704-9
3596:
3595:
3461:Ferroelectric RAM
3406:
3059:
2943:
2905:
2841:
2772:
2766:
2641:
2633:
2541:
2472:
2380:
2062:
1901:
1756:
1718:
1654:
1476:Linear elasticity
1460:phase field model
1289:
1071:
982:
848:
759:
649:
583:lithium tantalate
483:
482:
421:non pyroelectric
300:Curie temperature
253:ferroelectric RAM
215:Curie temperature
83:
82:
75:
16:(Redirected from
5098:
5091:Phases of matter
5055:ferrielectricity
5040:ferroelectricity
5012:
5005:
4998:
4989:
4968:
4949:
4927:
4900:
4899:
4881:
4871:
4839:
4833:
4832:
4830:
4828:cond-mat/0609347
4818:
4812:
4811:
4801:
4775:
4746:
4740:
4739:
4732:
4726:
4725:
4723:
4721:
4706:
4700:
4699:
4697:
4695:
4685:
4676:
4670:
4669:
4658:
4652:
4651:
4623:
4617:
4610:
4604:
4603:
4602:
4601:
4568:
4562:
4561:
4553:
4547:
4546:
4536:
4512:
4506:
4505:
4485:
4479:
4478:
4457:
4451:
4450:
4416:
4410:
4409:
4399:
4375:
4369:
4368:
4334:
4325:
4319:
4318:
4282:
4276:
4275:
4273:
4256:(8): 4537â4545.
4241:
4232:
4231:
4203:
4197:
4196:
4168:
4162:
4161:
4159:
4127:
4121:
4120:
4092:
4086:
4085:
4050:
4011:
3978:(7104): 759â65.
3968:
3957:10.1038/nmat1805
3937:Nature Materials
3928:
3922:
3921:
3895:
3893:cond-mat/0502109
3886:(24): 246802â4.
3875:
3869:
3868:
3842:
3840:cond-mat/0503372
3818:
3812:
3811:
3793:
3787:
3786:
3760:
3754:
3745:
3739:
3738:
3736:
3696:
3663:
3657:
3656:
3638:
3632:
3631:
3609:
3576:
3558:
3529:Flexoelectricity
3525:
3503:Piezoelectricity
3499:
3457:
3441:
3423:
3421:
3420:
3415:
3407:
3405:
3403:
3398:
3385:
3378:
3377:
3367:
3329:
3327:
3326:
3321:
3318:
3313:
3304:
3303:
3290:
3285:
3276:
3275:
3263:
3262:
3253:
3249:
3248:
3247:
3227:
3226:
3214:
3213:
3194:
3192:
3191:
3186:
3178:
3177:
3164:
3159:
3150:
3149:
3136:
3131:
3122:
3121:
3109:
3108:
3099:
3095:
3094:
3093:
3073:
3072:
3060:
3058:
3057:
3056:
3043:
3032:
3002:
3000:
2999:
2994:
2992:
2991:
2982:
2981:
2968:
2963:
2954:
2953:
2944:
2936:
2930:
2925:
2916:
2915:
2906:
2898:
2892:
2887:
2878:
2874:
2873:
2872:
2852:
2851:
2842:
2834:
2783:
2781:
2780:
2775:
2773:
2771:
2765:
2764:
2755:
2754:
2750:
2743:
2742:
2728:
2727:
2717:
2716:
2708:
2707:
2688:
2686:
2685:
2680:
2672:
2671:
2652:
2650:
2649:
2644:
2642:
2640:
2636:
2634:
2632:
2628:
2621:
2620:
2606:
2605:
2596:
2595:
2579:
2574:
2565:
2560:
2559:
2542:
2540:
2539:
2538:
2522:
2520:
2512:
2511:
2489:
2487:
2486:
2481:
2479:
2475:
2473:
2471:
2467:
2460:
2459:
2445:
2444:
2435:
2434:
2418:
2413:
2404:
2399:
2398:
2381:
2379:
2378:
2377:
2361:
2355:
2350:
2328:
2326:
2325:
2320:
2311:
2306:
2297:
2296:
2283:
2278:
2269:
2268:
2256:
2252:
2251:
2250:
2230:
2229:
2188:
2186:
2185:
2180:
2178:
2174:
2172:
2167:
2158:
2157:
2144:
2139:
2130:
2129:
2117:
2113:
2112:
2111:
2091:
2090:
2076:
2075:
2063:
2061:
2060:
2059:
2046:
2035:
2017:
2015:
2014:
2009:
2006:
2001:
1992:
1991:
1978:
1973:
1964:
1963:
1951:
1950:
1941:
1937:
1936:
1935:
1915:
1914:
1902:
1900:
1899:
1898:
1885:
1874:
1862:
1860:
1859:
1854:
1852:
1851:
1835:
1833:
1832:
1827:
1825:
1824:
1812:
1811:
1792:
1790:
1789:
1784:
1781:
1776:
1767:
1766:
1757:
1749:
1743:
1738:
1729:
1728:
1719:
1711:
1705:
1700:
1691:
1687:
1686:
1685:
1665:
1664:
1655:
1647:
1612:
1610:
1609:
1604:
1596:
1595:
1579:
1577:
1576:
1571:
1563:
1562:
1546:
1544:
1543:
1538:
1530:
1529:
1513:
1511:
1510:
1505:
1497:
1496:
1457:
1455:
1454:
1449:
1447:
1446:
1428:
1427:
1412:
1411:
1359:
1357:
1356:
1351:
1349:
1344:
1339:
1329:
1324:
1314:
1309:
1300:
1299:
1290:
1282:
1276:
1272:
1268:
1267:
1263:
1261:
1256:
1243:
1238:
1223:
1218:
1206:
1202:
1200:
1195:
1182:
1177:
1162:
1157:
1145:
1141:
1139:
1134:
1121:
1116:
1101:
1096:
1082:
1081:
1072:
1064:
1058:
1054:
1050:
1048:
1043:
1030:
1025:
1012:
1007:
993:
992:
983:
975:
969:
965:
961:
959:
954:
944:
939:
926:
921:
911:
906:
893:
888:
878:
873:
859:
858:
849:
841:
835:
831:
827:
825:
820:
807:
802:
789:
784:
770:
769:
760:
752:
747:
743:
741:
736:
723:
718:
705:
700:
686:
682:
681:
680:
660:
659:
650:
642:
610:Taylor expansion
542:phase transition
380:
352:piezoelectricity
317:energy harvester
265:piezoelectricity
86:Ferroelectricity
78:
71:
67:
64:
58:
38:
37:
30:
21:
5106:
5105:
5101:
5100:
5099:
5097:
5096:
5095:
5066:
5065:
5064:
5059:
5050:helielectricity
5035:paraelectricity
5021:
5016:
4975:
4965:
4952:
4946:
4930:
4924:
4911:
4908:
4906:Further reading
4903:
4841:
4840:
4836:
4820:
4819:
4815:
4748:
4747:
4743:
4734:
4733:
4729:
4719:
4717:
4708:
4707:
4703:
4693:
4691:
4683:
4678:
4677:
4673:
4660:
4659:
4655:
4648:10.1063/1.91359
4634:(11): 899â901.
4625:
4624:
4620:
4611:
4607:
4599:
4597:
4595:
4570:
4569:
4565:
4555:
4554:
4550:
4514:
4513:
4509:
4487:
4486:
4482:
4459:
4458:
4454:
4439:
4418:
4417:
4413:
4377:
4376:
4372:
4332:
4327:
4326:
4322:
4292:
4288:
4284:
4283:
4279:
4243:
4242:
4235:
4205:
4204:
4200:
4170:
4169:
4165:
4136:Surface Science
4129:
4128:
4124:
4094:
4093:
4089:
4051:
4025:(5733): 391â2.
4013:
3969:
3930:
3929:
3925:
3877:
3876:
3872:
3820:
3819:
3815:
3808:
3795:
3794:
3790:
3783:
3762:
3761:
3757:
3746:
3742:
3705:Physical Review
3698:
3673:Physical Review
3666:
3664:
3660:
3653:
3640:
3639:
3635:
3628:
3611:
3610:
3606:
3602:
3597:
3574:
3556:
3523:
3520:Ferroelasticity
3509:Pyroelectricity
3497:
3494:Paraelectricity
3455:
3438:
3430:
3386:
3369:
3368:
3361:
3360:
3354:
3350:
3345:
3338:
3295:
3267:
3254:
3239:
3232:
3228:
3218:
3205:
3200:
3199:
3169:
3141:
3113:
3100:
3085:
3078:
3074:
3064:
3048:
3044:
3033:
3026:
3025:
3020:
3016:
3009:
2983:
2973:
2945:
2907:
2864:
2857:
2853:
2843:
2819:
2818:
2813:
2809:
2804:
2800:
2794:
2790:
2756:
2734:
2733:
2729:
2719:
2718:
2699:
2694:
2693:
2663:
2658:
2657:
2612:
2611:
2607:
2597:
2587:
2551:
2547:
2543:
2530:
2526:
2503:
2498:
2497:
2451:
2450:
2446:
2436:
2426:
2390:
2386:
2382:
2369:
2365:
2337:
2336:
2288:
2260:
2242:
2235:
2231:
2221:
2216:
2215:
2209:
2197:
2149:
2121:
2103:
2096:
2092:
2082:
2081:
2077:
2067:
2051:
2047:
2036:
2023:
2022:
1983:
1955:
1942:
1927:
1920:
1916:
1906:
1890:
1886:
1875:
1868:
1867:
1843:
1838:
1837:
1816:
1803:
1798:
1797:
1758:
1720:
1677:
1670:
1666:
1656:
1632:
1631:
1625:
1587:
1582:
1581:
1554:
1549:
1548:
1521:
1516:
1515:
1488:
1483:
1482:
1432:
1416:
1403:
1398:
1397:
1382:
1375:
1368:
1347:
1346:
1291:
1274:
1273:
1229:
1225:
1168:
1164:
1107:
1103:
1087:
1083:
1073:
1056:
1055:
998:
994:
984:
967:
966:
864:
860:
850:
833:
832:
775:
771:
761:
691:
687:
672:
665:
661:
651:
639:
621:
620:
602:
549:liquid crystals
499:electric fields
495:barium titanate
492:
488:
454:
447:
439:
396:centrosymmetric
365:among which 32
356:pyroelectricity
347:
269:pyroelectricity
237:
230:
223:
137:
109:magnetic moment
79:
68:
62:
59:
51:help improve it
48:
39:
35:
28:
23:
22:
15:
12:
11:
5:
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5000:
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4973:External links
4971:
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4907:
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4752:Rabe, Karin M.
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4179:(16): 166101.
4163:
4122:
4103:(2): 342â343.
4087:
3923:
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3813:
3806:
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3782:978-0387765402
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3753:1997, New York
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524:Ferroelectric
490:
486:
481:
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470:
459:
452:
445:
437:
431:
430:
427:
426:ferroelectric
423:
422:
419:
412:
411:
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406:
399:
398:
392:
388:
387:
346:
343:
236:
233:
228:
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136:
133:
117:Joseph Valasek
105:ferromagnetism
81:
80:
63:September 2010
42:
40:
33:
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
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4438:9783527807505
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4304:
4300:
4296:
4281:
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4272:
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4259:
4255:
4251:
4250:ACS Catalysis
4247:
4240:
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4234:
4229:
4225:
4221:
4217:
4213:
4209:
4202:
4199:
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4141:
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4123:
4118:
4114:
4110:
4106:
4102:
4098:
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4079:
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4059:
4055:
4048:
4044:
4040:
4036:
4032:
4028:
4024:
4020:
4016:
4015:Spaldin, N.A.
4009:
4005:
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3989:
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3587:
3584:
3581:
3578:
3572:
3569:
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3566:
3562:
3554:
3553:Multiferroics
3551:
3548:
3545:
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3536:
3533:
3530:
3527:
3521:
3518:
3516:
3513:
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3433:
3427:
3425:
3411:
3408:
3400:
3395:
3391:
3382:
3374:
3358:
3357:local maximum
3346:
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3306:
3300:
3296:
3292:
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3272:
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3233:
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3197:
3182:
3179:
3174:
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3156:
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3142:
3138:
3133:
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3118:
3114:
3110:
3105:
3101:
3096:
3090:
3086:
3082:
3079:
3075:
3069:
3065:
3061:
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3022:
3012:
2988:
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2805:
2768:
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2692:
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2629:
2625:
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2598:
2592:
2588:
2584:
2581:
2576:
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2516:
2513:
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2265:
2261:
2257:
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2239:
2236:
2232:
2226:
2222:
2214:
2213:
2212:
2210:
2203:
2199:
2175:
2169:
2164:
2160:
2154:
2150:
2146:
2141:
2136:
2132:
2126:
2122:
2118:
2114:
2108:
2104:
2100:
2097:
2093:
2087:
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2078:
2072:
2068:
2064:
2056:
2052:
2043:
2031:
2028:
2021:
2020:
2003:
1998:
1994:
1988:
1984:
1980:
1975:
1970:
1966:
1960:
1956:
1952:
1947:
1943:
1938:
1932:
1928:
1924:
1921:
1917:
1911:
1907:
1903:
1895:
1891:
1882:
1866:
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1864:
1848:
1844:
1821:
1817:
1813:
1808:
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1778:
1773:
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1534:
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1395:
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1341:
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1311:
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615:
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565:
564:nitrous oxide
561:
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538:ferromagnetic
536:, much as do
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507:lead titanate
504:
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371:piezoelectric
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329:piezoelectric
326:
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291:
290:multiferroics
286:
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250:
245:
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208:magnetization
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201:
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189:
184:
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132:
130:
129:multiferroics
126:
122:
118:
114:
113:Rochelle salt
110:
106:
102:
98:
97:piezoelectric
94:
91:
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41:
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4935:
4932:Karin M Rabe
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3933:Spaldin, N.A
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375:pyroelectric
363:space groups
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235:Applications
225:
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181:permittivity
177:paraelectric
172:
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135:Polarization
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560:David Field
415:10 classes
402:20 classes
188:entrainment
90:spontaneous
5070:Categories
5030:dielectric
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4600:2022-09-22
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3600:References
2192:Since the
463:Tourmaline
313:desorption
311:to strong
309:adsorption
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